非线性全局优化问题填充函数法的研究

发布时间：2018-04-01 07:11

本文选题：全局优化　切入点：局部极小点　出处：《重庆大学》2016年硕士论文

【摘要】：最优化在实际生活中普遍存在,它是一个应用非常广泛的数学分支,随着科技的发展和社会的进步,最优化在工程设计、交通运输、生产管理、经济计划等方面都有着很大量的运用。全局优化问题主要有两个困难:一是怎样自通过局部优化已经得到的一个局部极小解去寻找更加优的局部极小解;二是如何判断目前的局部极小解是全局极小解。全局优化大致分为两个类型:一是确定性算法;二是随机性算法。其中,填充函数法是一种非常有效的第一类型的算法,它最先是由Ge[23]提出的,主要是解决上面提到的第一个困难。它的根本思想是在通过局部优化得到的局部极小点处构造一个关于目标函数的复合函数,称之为填充函数,利用该复合函数使目标函数离开目前的局部极小点,从而找到更加优的局部极小点。填充函数法借助了局部极小化算法,而局部优化理论和算法都发展的相当完善,于是填充函数法得到了广大最优化研究者的推崇,其算法关键在于填充函数的构造。全文分为五章:第一章简单地阐述了研究最优化以及非光滑优化重要性,然后给出了最优化方面本文需要的相关的基础定义,之后详细说明了在全局优化问题当中,填充函数法的产生背景和发展前景,并分析了学者们提出的填充函数的优缺点。第二章在无约束优化问题中,根据文献[46]给出的经典的填充函数的定义,给出了一个连续可微的单参数填充函数,克服了文献[23,46,70]中的填充函数出现指数项和文献[59,72,73]中填充函数在*f(x)?f(x)时不出现目标函数的任何信息的缺点。第三章根据文献[71]给定的有别于经典定义[46]的一种新的有效定义,在该新的定义上提出了一个新的单参数填充函数,另外克服了文献[71]中的函数在)()(*xfxf?时是不连续的缺陷。第四章首先给出了非光滑优化方面的一些基础知识,在非光滑无约束全局优化中,构造了一个双参数填充函数,实际上该函数可以视为单参数,相比文献[69],该函数得到了一定的改善,填充函数没有指数项。第五章对本文做了总结并对展望了填充函数法的发展。
[Abstract]:Optimization is a widely used branch of mathematics in real life. With the development of science and technology and social progress, optimization in engineering design, transportation, production management, The global optimization problem has two main difficulties: one is how to find a more optimal local minima solution by means of a local minima solution that has been obtained by local optimization; The second is how to judge that the local minima is a global minima. The global optimization can be divided into two types: one is deterministic algorithm, the other is randomness algorithm, in which the fill function method is a very effective first type algorithm. It was first put forward by GE [23], mainly to solve the first difficulty mentioned above. Its basic idea is to construct a compound function about the objective function at the local minima obtained by local optimization, which is called filling function. The compound function is used to make the objective function leave the current local minima, thus finding a more optimal local minima. The filling function method uses the local minimization algorithm, and the local optimization theory and algorithm are developed perfectly. Therefore, the filling function method is highly praised by the majority of optimization researchers, and the key of its algorithm lies in the construction of the filling function. The paper is divided into five chapters: chapter one simply describes the importance of studying optimization and non-smooth optimization. Then it gives the basic definition of optimization in this paper, and then explains the background and development prospect of the filling function method in the global optimization problem in detail. The advantages and disadvantages of the filling function proposed by scholars are analyzed. In the second chapter, according to the classical definition of filling function given in [46], a continuous differentiable single parameter filling function is given in the unconstrained optimization problem. It overcomes the occurrence of exponential term in the filling function in [23] and the filling function in [59 ~ 722 ~ (73)]. In chapter 3, according to a new effective definition given in reference [71], different from the classical definition [46], a new one-parameter filling function is proposed in this new definition. In addition, it overcomes the function in [71]. In chapter 4, we first give some basic knowledge of non-smooth optimization. In non-smooth unconstrained global optimization, we construct a two-parameter filling function. In fact, this function can be regarded as a single parameter. Compared with the reference [69], this function has been improved, and the filling function has no exponential term. In Chapter 5, the author summarizes this paper and looks forward to the development of the filling function method.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O224

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